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Question
If |x − 1| > 5, then ______.
Options
x ∈ (–4, 6)
x ∈ [–4, 6]
x ∈ [–∞, –4) ∪ (6, ∞)
x ∈ [–∞, –4) ∪ [6, ∞)
Solution
If |x −1| > 5, then x ∈ [–∞, – 4) ∪ (6, ∞).
Explanation:
Given that |x − 1| > 5
⇒ (x – 1) < –5 or (x – 1) > 5
⇒ x < –5 + 1 or x > 5 + 1
⇒ x < –4 or x > 6
⇒ x ∈ [–∞, –4) ∪ (6, ∞)
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